Hi Ryan,
That's always a tough one: keep something that has some history but also has a big flaw, or start afresh. I would say that if you expect or aim to receive far more than 7,300 video videos in the long run, and wish to attract many more than 31 subscribers, start again. This is also assuming that the channel is not particularly old, or doesn't have many traditional links itself.
The channel name is going to help your SEO if it's a good one, but I fear the branding is the main concern here. You will have a far harder time establishing trust and authority if you have a "random" user name, rather than something recognisable.